In order to understand and evaluate materials for use in lithium ion rechargeable battery electrodes, we have modeled the crystal structures of various manganese oxide and lithium manganese oxide compounds. We have modeled the MnO2 polymorphs and several spinels with intermediate compositions based on the amount of lithium inserted into the tetrahedral site. Three-dimensional representations of the structures provide a basis for identifying site occupancies, coordinations, manganese valence, order-disorder, and potentially new dopants for enhanced cathode behavior. X-ray diffraction simulations of the crystal structures provide good agreement with observed patterns for synthesized samples. Ionic modeling of these materials consists of an energy minimization approach using Coulombic, repulsive, and van der Waals interactions. Modeling using electronic polarizabilities (shell model) allows a systematic analysis of changes in lattice energy, cell volume, and the relative stability of doped structures using ions such as aluminum, titanium, nickel, and cobalt.